An algorithm for the superresolution of the sources of narrow-band signals on the basis of a solution of a system of observation equations
Igor Y. Anikin, Alexander M. Gruzlikov, Gleb B. Sidelnikov · Acoustical Physics · 2014
An algorithm for the superresolution of the sources of narrow-band signals on the basis of the solution of a system of observation equations is proposed. In accordance with this algorithm, the angular coordinates of sources are the roots of a single equation. To reliably estimate the coordinates, the number of time samples of observed signals must exceed the number of sources by at least one. In the case of a linear equidistant antenna array, a stable estimate of the angular coordinates requires that the number of time samples exceed the half-number of sources by at least one. A partial solution that provides minimization of the variance of the estimate errors is selected from the general solution. When the number of time samples that are used to estimate angular coordinates increases, the mathematical expectations of their errors tend to zero and the variances are larger than the minimally possible ones (determined from the Rao-Kramer inequality) by a factor of 1–1.2.